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Wednesday, April 5, 2017

Fibonacci and Golden Ratio Madness

The first reviews of my new book Finding Fibonacci have just come out, and I
have started doing promotional activities to try to raise awareness. As I expected, one of the first reviews I saw featured a picture of the Nautilus shell (no
connection to Fibonacci or the Golden Ratio), and media interviewers have
inevitably tried to direct the conversation towards the many fanciful—but for the
most part totally bogus—claims about how the Golden Ratio (and hence the
Fibonacci sequence) are related to human aesthetics, and can be found in a
wide variety of real-world objects besides the Nautilus shell. [Note: the Fibonacci
sequence absolutely is mathematically related to the Golden Ratio. That’s one of
the few golden ratio claims that is valid! There is no evidence Fibonacci knew of
the connection.]

For some reason, once a number has been given names like “Golden Ratio” and
“Divine Ratio”, millions of otherwise sane, rational human beings seem willing to
accept claims based on no evidence whatsoever, and cling to those beliefs in the
face of a steady barrage of contrary evidence going back to 1992, when the
University of Maine mathematician George Markovsky published a seventeen-
page paper titled "Misconceptions about the Golden Ratio" in the MAA’s
College Mathematics Journal, Vol. 23, No. 1 (Jan. 1992), pp. 2-19.

I first entered the fray with a Devlin’s Angle post in June 2004 titled "Good Stories
Pity They’re Not True" [the MAA archive is not currently accessible], and then
again in May 2007 with "The Myth That Will Not Go Away" [ditto].

Those two posts gave rise to a number of articles in which I was quoted, one of
the most recent being "The Golden Ration: Design’s Biggest Myth," by John
Brownlee, which appeared in Fast CompanyDesign on April 13, 2015.

In 2011, the Museum of Mathematics in New York City invited me to give a public
lecture titled "Fibonacci and the Golden Ratio Exposed: Common Myths andFascinating Truths," the recording of which was at the time (and I think still is) the
most commented-on MoMath lecture video on YouTube, largely due to the many
Internet trolls the post attracted—an observation that I find very telling as to the
kinds of people who hitch their belief system to one particular ratio that does not
quite work out to be 1.6 (or any other rational number for that matter), and for
which the majority of instances of those beliefs are supported by not one shred of
evidence. (File along with UFOs, Flat Earth, Moon Landing Hoax, Climate
Change Denial, and all the rest.)

Needless to say, having been at the golden ratio debunking game for many years
now, I have learned to expect I’ll have to field questions about it. Even in a media
interview about a book that, not only flatly refutes all the fanciful stuff, but lays out
the history showing that the medieval mathematician known today as Fibonacci
left no evidence he had the slightest interest in the sequence now named after
him, nor had any idea it had several cute properties. Rather, he simply included
among the hundreds of arithmetic problems in his seminal book Liber abbaci,
published in 1202, an ancient one about a fictitious rabbit population, the solution
of which is that sequence.

What I have always found intriguing is the question, how did this urban legend
begin? It turns out to be a relatively recent phenomenon. The culprit is a German
psychologist and author called Adolf Zeising. In 1855, he published a book titled: A New Theory of the proportions of the human body, developed from a basic
morphological law which stayed hitherto unknown, and which permeates the
whole nature and art, accompanied by a complete summary of the prevailing
systems.

This book, which today would likely be classified as “New Age,” is where the
claim first appears that the proportions of the human body are based on the
Golden Ratio. For example, taking the height from a person's naval to their toes
and dividing it by the person's total height yields the Golden Ratio. So, he claims,
does dividing height of the face by its width.

From here Zeising leaped to make a connection between these human-centered
proportions and ancient and Renaissance architecture. Not such an
unreasonable jump, perhaps, but it was, and is pure speculation. After Zeising,
the Golden Ratio Thing just took off.

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